Journal of the Mathematical Society of Japan

A note on the dimensions of Assouad and Aikawa

Juha LEHRBÄCK and Heli TUOMINEN

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Abstract

We show that in Euclidean space and other regular metric spaces, the notions of dimensions defined by Assouad and Aikawa coincide. In addition, in more general metric spaces, we study the relationship between these two dimensions and a related codimension and give an application of the Aikawa (co)dimension for the Hardy inequalities.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 2 (2013), 343-356.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1366896636

Digital Object Identifier
doi:10.2969/jmsj/06520343

Mathematical Reviews number (MathSciNet)
MR3055588

Zentralblatt MATH identifier
1279.54022

Subjects
Primary: 54F45: Dimension theory [See also 55M10]
Secondary: 28A12: Contents, measures, outer measures, capacities 54E35: Metric spaces, metrizability 26D15: Inequalities for sums, series and integrals

Keywords
Assouad dimension Aikawa dimension metric space doubling measure Hardy inequality

Citation

LEHRBÄCK, Juha; TUOMINEN, Heli. A note on the dimensions of Assouad and Aikawa. J. Math. Soc. Japan 65 (2013), no. 2, 343--356. doi:10.2969/jmsj/06520343. https://projecteuclid.org/euclid.jmsj/1366896636


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